choice c:
fatal change of meaning.
this sentence implies that we are currently 'forcing [these species] to become extinct', a meaning that not only differs from the original but also borders on absurdity.
the original meaning, which we're not allowed to change, is that humans have forced the species into extinction at some point in the last 500 years, not that humans are doing so currently.

'to become extinct' does seem, to my eyes, more awkward and wordy than 'to extinction', but there are other issues in choices b and c.

choice b:
biggest problem = incorrect idiom: 'known as having forced'
known as is used with nouns: al capone was known as a gangster rather than as a tax cheat, but he was ultimately imprisoned only on charges of tax evasion.

with verbs, you have to use 'known to infinitive' or 'known for gerund'.